I don't think "shared knowledge" means "shared knowledge between mathematicians and lay persons" (there is no much point in that, the same way a smartphone technician knows how a smartphone works deep down to the details but there is no big interest for society to have every lay persons being informed about it). I think it means "shared knowledge between mathematicians".

And at this level, while there are anecdotical exceptions, mathematicians have always been pretty decent (with their conferences, workshops, paper publications, international collaborations, ...).

So, it does not mean "teaching the subject", it means "creating a human network of people that share the understanding". LLM can be useful at telling a human, but you still need a human. The point of Tao is not that LLM is not good at providing explanations, it is that "providing explanations" is not the contribution to science, "the human network" is. It's like saying "LLM are great cook, they generate tons of food in space", but the point of having cooks is so that people can eat food and not die. Having LLM generating mathematical proofs is as useless as having LLM generating food that no one can access: the point was never to "generate proofs" or "generate food", the point was "creating a shared human understanding" or "eating the food so human can survive".

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tossandthrow 3 hours ago | parent [-]

I don't get the argument.

I get that there is a cultural benefit to keeping it alive. Just like we ideally want the languages represented at the universities.

But keeping humans in the loop does not appear to be necessary in order to call it science, and certainly not in order to have progress or dessiminate that progress.

I don't have a problem with people doing math. As long that we don't idiomatically hold on to that way of doing things.

I do, however, find it hard to belive that individual humans will play a big role from here and forward, in any scientific desciplines.

	▲	cauch 2 hours ago \| parent [-]
		The goal is indeed to have progress or disseminate that progress. The point of Tao is that people see LLM providing "proofs" and are concluding that this is all that is needed to "have progress or disseminate that progress". That is the same mistake of thinking that "generating food" is all that is needed to "have people not dying of hunger". The hard part of "have progress or disseminate that progress" is the human network. A fundamental point of this human network is that it generate trust, accountability and reliability. Generating "useful new theorem" is useless unless the society also built the trust around the theorem to distinguish it from a fake theorem. Maybe in the future, we will have AI doing some part of it, but this is a totally different AI animal than the one we are able to have now, and people who think the current AI that we see now is able to do that have no understanding how it works. This is demonstrated by the facts in math: current AI is able to provide math proofs, and yet, a lot of human work is still needed to get progress out of current AI. I would not bet that individual humans will still play a role as big as today in the future. Maybe AI will be different in the future, but the reality is that we don't have any indication if this is even possible.